Nooooo, A Fender 62 jazz in a gig bag on a plane? please don't make us cry at the thought.
My Ibenez is not close to 10% of what your 62 Fender is worth and I carry it in a hard case. I had my 18" enclosure rolled over onto the hard case.
Even if you have DL status and is able to board early and find a bin that can hold your baby there is no guarantee that someone will just toss their carry on in there.
I am fortunate that my bass flying are all TPAC on the 747/777 where there are more options for a bass in a hard case carried on.
Plan for the worse case. Best bet are the shipping quality hard cases; worse case is that you will be asked to check it. I have not use it but one my local music rental shop has Anvil bass guitar shipping case for rent.
I pray that you will not have to write the bass version of this song:
http://www.youtube.com/watch?v=5YGc4zOqozo